Sol'n: Since the load is varies along the length of the column, integration is used. The best approach is to convert all lengths and units to inches and integrate the elongations of each infinitesimal length dx:

• A(x) = constant = p(42 in.)²/4 = 1385 in²
• E(x) = constant = 2.5 Msi
• P(x) on an element dx which is at a distance of x from the top of the column is:
       - P(x) = (Volume)(Density) = ––rAx ... P is a compressive force.
       - r = 0.0839 lb/in.³

Integrating gives the change in length:

D = –0.00151 in. (negative since a column in compression shortens)

Thus, the downward displacement of the top of the column is:

d = 0.00151 in. (positive - positive value down)